If $f(x) = 4-3x$ and $g(x) = x^2 +1$, find $f(g(\sqrt{2}))$.
Solution: We have that
$$g(\sqrt{2}) = (\sqrt{2})^2 + 1 = 2 +1 = 3.$$Then,
$$f(g(\sqrt{2})) = f(3) = 4 - 3(3) = 4 - 9 = \boxed{-5}.$$